Optimal. Leaf size=35 \[ \text {Int}\left (\frac {\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{\sqrt {g+h x}},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.31, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{\sqrt {g+h x}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{\sqrt {g+h x}} \, dx &=\int \frac {\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{\sqrt {g+h x}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 2.07, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{\sqrt {g+h x}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}}{\sqrt {h x + g}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.35, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )+a}}{\sqrt {h x +g}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}}{\sqrt {h x + g}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {\sqrt {a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )}}{\sqrt {g+h\,x}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}}}{\sqrt {g + h x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________